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Maths / Comparing Quantities / Finding Cost Price
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Finding Cost Price

To Find Cost Price when Profit/Loss percent is given: The procedure to find the cost price when profit/loss % is given is as follows:

Step I: We will assume the Cost Price to be x.

Step II: Then we find the Profit/Loss on the cost price

Strep III: We will equate the equation with the given Selling Price.

Step IV: We will solve for x.

Profit/ Loss = frac{Profit/Loss%}{100}times Cost ;Price

Selling Price = Cost Price + Profit

Selling Price = Cost Price- Loss

Illustration 1: Mrs Rohana sold a dress for Rs 495 thus making a profit of 10%. Find the cost price of the dress and the profit ?

Solution:  Let the Cost Price of the dress  = x Rs.

      Profit % = 10%

       Profit = 10 % of x

                small =frac{10}{100}times x = frac{x}{10};Rs

      Selling Price = Cost Price + Profit

                  small 495 = x + frac{x}{10}

                   small 495 = frac{10x+x}{10}

                  4950 = 11x

                 x=frac{4950}{11}

                 x = Rs. 450

Hence, Cost price = Rs 450

Now, as we know that     

Profit = Selling Price - Cost Price

Profit = 495 - 450

        = Rs 45

Illustration 2: A man purchases two fans for Rs 2160. By selling one fan at a profit of 15 % and the other at a loss of 9 % he neither gains nor loses in the whole transaction. Find the cost price of each fan.

Solution: Let the C.P. of the first fant be Rs x. Then,

C.P. of the second fan = Rs(2160 - x)

As it is given that in the whole transaction, the man neither gains nor loses.

therefore  Gain on the sale of first fan = Loss in the sale of second fan

Rightarrow 15;of; Rs x =9%;of;Rs(2160 -x)

Rightarrow frac{15}{100}times x=frac{9}{100}times (2160-x)

Rightarrow 15x=9(2160-x)

Dividing both sides by 3

Rightarrow 5x=3(2160-x)

Rightarrow 5x=6480-3x

Rightarrow 5x+3x=6480

Rightarrow 8x=6480

Rightarrow x=frac{6480}{8}

Rightarrow x=810

So, C.P. of first fan = Rs 810

C.P. of second fan = Rs(2160 - x) = Rs (2160 - 810)

                           = Rs 1350


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